Question

The equation of thermodynamic state of an ideal gas can be expressed as $(P+\frac{a}{V^2})(V-b)=RT$. Here, $P$ is the pressure, $V$ is the volume, $T$ is the absolute temperature and $a,b,$ and $R$ are constants. Which of the following options correctly represents the dimension of $a$?

• A. $\left[M{L}^5{T}^{-2}\right]$
• B. $\left[M{L}^{-1}{T}^{-2}\right]$
• C. $\left[M^0{L}^3{T}^0\right]$
• D. $\left[M^0{L}^6{T}^0\right]$

Answer 1

The correct option is A $\left[M{L}^5{T}^{-2}\right]$

$\frac{a}{V^2}$ term has been added to pressure $P$.
$\Rightarrow \frac{a}{V^2}$ must have unit of pressure.
$\Rightarrow \left[P\right]=\left[\frac{a}{V^2}\right]$
$\Rightarrow \left[M{L}^{-1}{T}^{-2}\right]=\frac{\left[a\right]}{\left(\right[M^0{L}^3{T}^0]{)}^2}$
$\Rightarrow \left[a\right]=\left[M{L}^5{T}^{-2}\right]$